Single Variable New First-Order Shear Deformation Plate Theory: Numerical Solutions of Lévy-Type Plates Using Fourth-Order Runge-Kutta Technique

Abstract

In this paper, numerical results for flexure of shear-deformable isotropic square plates by utilizing recently proposed single variable new first-order shear deformation plate theory (SVNFSDT) are presented. For obtaining numerical results, fourth-order Runge-Kutta technique is used. It should be noted that the displacement functions of SVNFSDT give rise to constant transverse shear strains and hence constant transverse shear stresses through the plate thickness. Hence, similar to other first-order shear deformation plate theories reported in the literature, this theory also requires a shear correction factor. As opposed to Mindlin plate theory, SVNFSDT has only one fourth-order governing differential equation which is obtained by utilizing plate gross equilibrium equations. This theory presents physically meaningful boundary conditions. On similar lines of two-dimensional theory of elasticity approach for beam analysis, this theory also presents two different types of plate clamped edge boundary conditions. Illustrative examples presented in this paper consider Levy-type plates with two opposite plate edges simply supported and remaining two plate edges having either simply supported, clamped, or free boundary conditions with plate under the action of uniformly distributed transverse load. Numerical results for flexure of abovementioned cases of plates are presented for different values of plate thickness-to-length ratio. In order to demonstrate the efficacy of the presented numerical solution technique, obtained results are compared with corresponding results reported in the literature.